Binary to decimal conversion Convert the binary number 01001110₂ to decimal (base 10).
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
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A4E
-
B78
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C76
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D116
Answer
Correct Answer: 78
Explanation
Introduction / Context:Converting binary to decimal requires summing the place values where bits are 1. This reinforces understanding of positional notation in base 2.
Given Data / Assumptions:
- Binary: 01001110₂.
- Bit weights from MSB to LSB: 128, 64, 32, 16, 8, 4, 2, 1.
Concept / Approach:Add the weights corresponding to the 1 bits in the binary string to obtain the decimal value.
Step-by-Step Solution:
1) Identify 1s at positions 64 (0), 32 (1), 16 (0), 8 (1), 4 (1), 2 (1), 1 (0).2) Sum: 32 + 8 + 4 + 2 = 46? (Recheck ordering): The string is 0 1 0 0 1 1 1 0.3) Weights with 1s: 64 (second bit) + 8 + 4 + 2 = 64 + 8 + 4 + 2 = 78.4) Therefore decimal value = 78.Verification / Alternative check:Interpret as hex first: 0100 1110₂ = 0x4E; convert 0x4E = 4*16 + 14 = 64 + 14 = 78.
Why Other Options Are Wrong:
- 4E: That is the hexadecimal form, not decimal.
- 76 / 116: Sum of selected weights does not equal these numbers for this bit pattern.
Common Pitfalls:Misaligning bit weights, confusing hex representation with decimal value, or forgetting the leading zero does not change value.
Final Answer:78